Prove that $(1+cotx)/cscx-secx/(tanx+cotx)=cosx$ ?

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Answer 1 · 2017-01-23T05:59:45

Please see below.

$(1+cotx)/cscx-secx/(tanx+cotx)$

= $(1+cosx/sinx)/(1/sinx)-(1/cosx)/(sinx/cosx+cosx/sinx)$

= $(sinx+cosx)-(1/cosx)/((sin^2x+cos^2x)/(sinxcosx)$

mutiplying numerator and denominator in first term by $sinx$

= $(sinx+cosx)-(1/cosx)/(1/(sinxcosx)$

= $(sinx+cosx)-1/cosx xxsinxcosx$

= $sinx+cosx-sinx$

= $cosx$

Prove that (1+cotx)/cscx-secx/(tanx+cotx)=cosx(1+cotx)/cscx-secx/(tanx+cotx)=cosx?